The disclosed subject matter relates to methods and systems for mechanical oscillators. Oscillators can produce continuous periodic signals from direct current (DC) power. Such oscillators can be utilized in communication systems, including, but not limited to, applications such as timing references and frequency modulators. Certain oscillators can include macroscopic mechanical resonators, such as quartz crystals, which can utilize unsuitably large off-chip space for certain applications.
Micro-electro-mechanical systems (MEMS) oscillators, which can be integrated on-chip, can demonstrate frequency stability and high resonant frequency, among other attributes. However, MEMS oscillators can occupy large footprints on integrated circuits level, and because they achieve high frequency through large mechanical stiffness, frequency tunability can be limited. Such MEMS oscillators are, therefore, not well suited for implementing voltage-controlled oscillators (VCOs). In contrast, Nano-electro-mechanical systems (NEMS) oscillators can achieve high resonant frequencies while maintaining mechanical compliance needed for tunability, and only require small on-chip area. The active area of the NEMS oscillators can be as small as 1 micron by 1 micron, compared to MEMS oscillators which typically occupy more than 100 microns by 100 microns. NEMS oscillators can exhibit resonant frequencies larger than 400 MHz in SiC beams and ˜14 MHz in AlN-based resonators, where both systems can be designed for high frequency stability and low phase noise, as opposed to frequency tunability. In addition, due to their small sizes, the motional impedance of NEMS can be large, which can cause its electro-mechanical signal to be overwhelmed by spurious coupling or background noise.
Graphene is an atomically thin, ultra-stiff, yet extremely strong material. Graphene can achieve high resonant frequencies that can be externally tuned over a wide range (up to ˜400%) with an application of moderate (<10 V) voltages across the suspended channel and the underlying gate. In addition, its electrically tunable conductance in conjunction with its large electrical mobility allows efficient transduction of mechanical vibration when a graphene membrane is configured as a suspended vibrating field-effect resonator. This can allow a direct radio-frequency (RF) electrical readout with signal to background ratios (SBR) larger than 20 dB at room temperature.